Multiplicative perturbation bounds for the block Cholesky downdating problem

ABSTRACT

In this paper, we give the explicit expressions for the strong and the weak rigorous multiplicative perturbation bounds for the block Cholesky downdating problem. First, we derived the strong rigorous multiplicative perturbation bounds by combining the modified matrix-vector equation approach with the strategy for Lyapunov majorant function and the Banach fixed point theorem. Then, the weak rigorous multiplicative bounds are obtained with the help of the matrix-equation approach. The obtained results are illustrated by numerical tests.

KEYWORDS:

• Block Cholesky downdating problem
• multiplicative perturbation
• Lyapunov majorant fuction
• Banach fixed point theorem
• matrix-equation approach
• rigorous perturbation bounds

AMS SUBJECT CLASSIFICATIONS:

• 15A23
• 15A45
• 65F35

Acknowledgments

The authors appreciate the constructive remarks and suggestions of the anonymous referees that helped to improve the paper.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The work is supported by the National Natural Science Foundation of China (Grant Nos. 11671060, 11571062, and 11771062).